Lord Grade: the Financial Times editor has suggested that the former BBC chairman be appointed as a mediator in the press regulation row. Photograph: Dan Kitwood/Getty Images

The Financial Times editor has proposed that Lord Grade, the former Channel 4 chief executive and BBC chairman, be appointed as a mediator to broker a deal between the newspaper industry and pressure group Hacked Off over a new press regulator.

Lionel Barber told a parliamentary select committee on Tuesday that a deal needed to be struck before September when the trials of current and former News International journalists and executives accused of phone hacking and illegal payments to public officials begin.

Barber said someone of Grade's experience and calibre was urgently needed to shift the impasse in talks. Grade, also a former ITV executive chairman who is currently chairman of Pinewood and Shepperton studios, started his media career as a sports journalist on the Daily Mirror and had been mentioned as the kind of all-rounder who would command respect of all sides in the dispute over the future of press regulation in a similar way to George Mitchell, the US special envoy sent to Northern Ireland to negotiate a peace settlement in the 1990s.

"His name has come up in conversations with one or two editors," Barber told MPs on the Commons culture, media and sport select committee. "You need someone who some experience of journalism, some experience of business and some political nous, and someone who is respected on all sides."

Lord Grade told the Guardian: "I haven't had any approach, but it is definitely very important that we get a consensus ASAP and if anyone thinks I can help I would be glad to."

Hacked Off, however, made it clear that it believed no negotiation or compromise was necessary and that the government should stick to the proposal agreed in March.

Evan Harris, associate director of Hacked Off, denied a compromise was needed just because the press didn't agree to that proposal.

"The banks didn't like regulation, they did not get to renegotiate," he said.

He also queried the credentials of Grade, pointing out he was a Tory peer who had a vested interest as he was a member of the PCC.

Grade said: "He is entitled to his opinion, of course, but this is premature as the idea [of a mediator] has just been floated."

Barber told MPs the outstanding differences between the various sides with an interest in press regulation were not "as big as some people like to make out" and a deal was achievable.

His suggestion that Grade be parachuted in to find a solution acceptable to both sides in the standoff will give fresh impetus to efforts to get a new regulator up and running this year.

"FT's @barberlionel suggests Michael Grade should be brought in to negotiate #Leveson settlement. I agree," he wrote.

A deal was struck on 18 March between all three main parties and Hacked Off for a replacement for the Press Complaints Commission backed by a royal charter.

But the late night deal was immediately denounced by many in the press industry, who claimed they had been locked out of negotiations. Three of the country's biggest newspaper groups – News International, Telegraph Media Group and Associated Newspapers – threatened to boycott the government's plans and set up their own regulator.

Since then these publishers, along with Trinity Mirror, Express Newspapers and most of the regional press and magazine sector, have come up with an alternative royal charter, but need the support of Hacked Off and politicians if it is to be put before the privy council.

One of the main issues of contention is the cost of the regulator proposed by the government. The industry believes that the proposal to inflict exemplary or punitive damages on publications guilty of egregious breaches of libel or privacy law could put titles out of business. They also argue that it could be against European human rights law.

Barber said the FT would look at the cost of joining any new press regulator before making a decision. "If it's too burdensome we won't join," he added.

Chris Blackhurst, the group content director at the Independent, told the same select committee hearing on Tuesday that if the cost of regulation rocketed it could lead to job losses.

Newspaper groups have been talking to the culture secretary, Maria Miller, over the past two months and to Hacked Off about breaking the impasse.

Barber said Hacked Off had "played a role" in negotiating a new regulator and it was important that the victims were "bound in and were part of the process". However, he added: "There needs to be give on all sides."

He said the newspaper industry had already made a major concession by agreeing to ditch its proposal to have a veto over appointments to the board of the new regulator.

Barber's hopes that all sides would give ground were dashed immediately after the select committee hearing when Hacked Off said there was no reason to reopen negotiations.

"There is no basis to compromise further," Hacked Off said in a statement. "Gerry McCann already called the Leveson recommendations the minimum acceptable compromise for victims of press mistreatment. Concessions in the cross-party charter, and the use of a royal charter itself instead of legislation have moved the deal in the press's favour.

"We have an agreement signed up to by all political parties and both houses of parliament, backed by the victims of press abuse and the vast majority of the general public. What are the grounds for reopening negotiations, simply because, as Leveson predicted, the press barons are reluctant to comply?"

• To contact the MediaGuardian news desk email media@theguardian.com or phone 020 3353 3857. For all other inquiries please call the main Guardian switchboard on 020 3353 2000. If you are writing a comment for publication, please mark clearly "for publication".

• To get the latest media news to your desktop or mobile, follow MediaGuardian on Twitter and Facebook